Question

find the degree of polynomial minus t to the power 9 plus 4 t to the power 6 plus 7 t to the power 5 divided t to the power 5?
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Answer 1

SOLUTION

TO DETERMINE

The degree of the polynomial

$\displaystyle \sf{ \frac{ - {t}^{9} + 4 {t}^{6} + 7 {t}^{5} }{ {t}^{5} } }$

CONCEPT TO BE IMPLEMENTED

POLYNOMIAL

Polynomial is a mathematical expression consisting of variables, constants that can be combined using mathematical operations addition, subtraction, multiplication and whole number exponentiation of variables

DEGREE OF A POLYNOMIAL

Degree of a polynomial is defined as the highest power of its variable that appears with nonzero coefficient

EVALUATION

Here the given mathematical expression is

$\displaystyle \sf{ \frac{ - {t}^{9} + 4 {t}^{6} + 7 {t}^{5} }{ {t}^{5} } }$

Now the above expression can be rewritten as

$\displaystyle \sf{ \frac{ - {t}^{9} + 4 {t}^{6} + 7 {t}^{5} }{ {t}^{5} } }$

$\displaystyle \sf{ = - {t}^{9 - 5} + 4 {t}^{6 - 5} + 7 {t}^{5 - 5} }$

$\displaystyle \sf{ = - {t}^{4} + 4 {t}^{1} + 7 {t}^{0} }$

$\displaystyle \sf{ = - {t}^{4} + 4 {t}^{} + 7 }$

Thus the variable is t

Now the highest power of its variable that appears with nonzero coefficient is 4

Hence the required degree of the polynomial = 4

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